A local adaptive method for the numerical approximation in seismic wave modelling

Bruno G. Galuzzi 1 , Elena Zampieri 2  and Eusebio M. Stucchi 3
  • 1 Department of Earth Sciences, University of Milan, , Milan, Italy
  • 2 Department of Mathematics, University of Milan, , Milan, Italy
  • 3 Department of Earth Sciences, University of Milan, , Milan, Italy


We propose a new numerical approach for the solution of the 2D acoustic wave equation to model the predicted data in the field of active-source seismic inverse problems. This method consists in using an explicit finite difference technique with an adaptive order of approximation of the spatial derivatives that takes into account the local velocity at the grid nodes. Testing our method to simulate the recorded seismograms in a marine seismic acquisition, we found that the low computational time and the low approximation error of the proposed approach make it suitable in the context of seismic inversion problems.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • 1. A. Tarantola, A strategy for nonlinear elastic inversion of seismic reection data, Geophysics, vol. 51, no. 10, pp. 1893-1903, 1986.

  • 2. J. Virieux and S. Operto, An overview of full-waveform inversion in exploration geophysics, Geophysics, vol. 74, no. 6, pp. WCC1-WCC26, 2009.

  • 3. R. Alford, K. Kelly, and D. M. Boore, Accuracy of finite-difference modeling of the acoustic wave equation, Geophysics, vol. 39, no. 6, pp. 834- 842, 1974.

  • 4. J. Virieux, V. Cruz-Atienza, R. Brossier, E. Chaljub, O. Coutant, S. Garambois, D. Mercerat, V. Prieux, S. Operto, A. Ribodetti, et al., Modelling seismic wave propagation for geophysical imaging. Intech, 2016.

  • 5. R. E. Sheriff and L. P. Geldart, Exploration seismology. Cambridge university press, 1995.

  • 6. Ö. Yilmaz, Seismic data analysis: Processing, inversion, and interpre- tation of seismic data. Society of exploration geophysicists, 2001.

  • 7. A. Fichtner, Full seismic waveform modelling and inversion: Springer science & business media, 2011.

  • 8. A. Sajeva, M. Aleardi, E. Stucchi, N. Bienati, and A. Mazzotti, Estimation of acoustic macro models using a genetic full-waveform inversion: Applications to the marmousi model, Geophysics, 2016.

  • 9. A. Tognarelli, E. Stucchi, N. Bienati, A. Sajeva, M. Aleardi, and A. Mazzotti, Two-grid stochastic full waveform inversion of 2d marine seismic data, in 77th EAGE Conference and Exhibition 2015, 2015.

  • 10. C. L. Liner, Theory of a 2.5-d acoustic wave equation for constant density media, Geophysics, vol. 56, no. 12, pp. 2114-2117, 1991.

  • 11. Z.-M. Song, P. R. Williamson, and R. G. Pratt, Frequency-domain acoustic-wave modeling and inversion of crosshole data: Part iiinversion method, synthetic experiments and real-data results, Geo- physics, vol. 60, no. 3, pp. 796-809, 1995.

  • 12. P. R. Williamson and R. G. Pratt, A critical review of acoustic wave modeling procedures in 2.5 dimensions, Geophysics, vol. 60, no. 2, pp. 591-595, 1995.

  • 13. A. R. Mitchell and D. F. Griffths, The finite difference method in partial differential equations. John Wiley, 1980. 14. K. W. Morton and D. F. Mayers, Numerical solution of partial differ- ential equations: an introduction. Cambridge university press, 2005.

  • 15. R. Richtmyer and K. Morton, Difference methods for initial-value problems. 1967, Interscience, New York.

  • 16. J. C. Strikwerda, Finite difference schemes and partial differential equa- tions. SIAM, 2004.

  • 17. G. C. Cohen, Higher-order numerical methods for transient wave equations, 2003.

  • 18. B. Fornberg, Generation of finite difference formulas on arbitrarily spaced grids, Mathematics of computation, vol. 51, no. 184, pp. 699- 706, 1988.

  • 19. C. Cerjan, D. Kosloff, R. Kosloff, and M. Reshef, A nonreecting boundary condition for discrete acoustic and elastic wave equations, Geo- physics, vol. 50, no. 4, pp. 705-708, 1985.

  • 20. R. Courant, K. Friedrichs, and H. Lewy, On the partial difference equations of mathematical physics, IBM journal of Research and Develop- ment, vol. 11, no. 2, pp. 215-234, 1967.

  • 21. C. E. Shannon, Communication in the presence of noise, Proceedings of the IRE, vol. 37, no. 1, pp. 10-21, 1949.

  • 22. C. Bunks, F. M. Saleck, S. Zaleski, and G. Chavent, Multiscale seismic waveform inversion, Geophysics, vol. 60, no. 5, pp. 1457-1473, 1995.

  • 23. A. Brougois, M. Bourget, P. Lailly, M. Poulet, P. Ricarte, and R. Versteeg, Marmousi, model and data, in EAEG Workshop-Practical Aspects of Seismic Data Inversion, 1990.


Journal + Issues